As was already noted by Barrat and Bocquet [1]}, a continuum approach is perfectly adequate to describe the hydrodynamics of fluids at a distance of more than a few molecular diameters from a surface.
However, in order to estimate the magnitude of the velocity profile close to the surface, a microscopic picture is needed.
In a sense, this fact is already clear from the long discussion about the meaning of the \(\zeta \) -potential in electro-kinetic flows: this quantity depends sensitively on the local fluidity and molecular arrangements near a surface and typically cannot be predicted with any accuracy on the basis of macroscopic arguments alone.
Moreover, even though the action of the surface is usually very local, its effect extends into the bulk as it changes the effective hydrodynamic boundary conditions [2]}.
